Energy of EM Radiation

[Anonymous No.11266416]

Can someone explain this to me? Why does energy depend only on squared amplitude for EM fields but only on frequency for photons when photons are EM field quanta? How are these two combined?

[Anonymous No.11266463]

>>11266416
You’re comparing a wave with a particle-wave. Each photon has a discrete energy; this is why it is called ‘quantum’ theory. When you increase the intensity of a light beam, you are increasing the amount of photons, which increases the energy.

[Anonymous No.11266492]

>>11266463
That's not my question. My question is how can you mathematically relate those two and why is there this apparent difference. I know how to derive both poynting vector from maxwell and photon energy from photoelectric effect or pic related. What I probably don't understand is how to express the poynting vector in terms of photons, also pic related.

[Anonymous No.11266511]

These are two different concepts. Asking why the energy in an EM-field depends only on the square of the amplitude is basically asking why energy is conserved - this is a law of nature. The quantity S is called poyntings vector.

The photon does not have a charge, really, so it does not produce a magnetic field the way moving charge does. Maybe theres a way in advanced quantum dynamics to assign a "magnetic field" to a photon, but the takeaway is that these are mostly unrelated concepts.

[Anonymous No.11266580]

>>11266492
>What I probably don't understand is how to express the poynting vector in terms of photons

The Pointing vector is the same thing as the momentum carried by the electromagnetic field. The momentum carried by a single photon is related to the wavenumber k, which is a vector with magnitude 2pi/lambda.

So if we have a plane wave where all the photons have the same k, we have the relation
[math]E\times B=n\hbar k[/math]

where I'm using units where the speed of light and the vacuum permittivity are set to 1, and the number of photons n, E, and B should all be considered averages since this is quantum.

[Anonymous No.11266595]

>>11266463
>he thinks 'photons' exist
oh no no no no

[Anonymous No.11266596]

>>11266580
Actually I realize the pointing vector is the momentum density, so that n should be considered the number *density* of photons, not the total number.

[Anonymous No.11266650]

>>11266595
>single photon sources don't exist
>detecting single photons is impossible
Are you a time traveler from 100 years ago?

[Anonymous No.11266658]

>>11266650
Photo detectors can be explained purely in terms of fields, the particle interpretation adds nothing. Similarly with the double slit and solid photoelectric effect, if anything the particle view muddies double slit. Gas phase photoelectric effect can't be explained in the particle view. Further, photons are not localized and so does not satisfy any meaningful definition of 'particle'. The particle view adds nothing and subtracts much. It's outdated.

[Anonymous No.11266666]

>>11266658
Do you have a reference that could perchance add some, lets say, relativistic mass to your argument?

[Anonymous No.11266677]

>>11266666
W. E. Lamb, Anti-photon

[Anonymous No.11266749]

>>11266416
Define one photon.

[Anonymous No.11266752]

>>11266416
Wait... So 1watt laser and 2watt laser have different frequency? Doubt.

What about realizing that interference is done due to viscosity, and there IS a substance it propagates trought.

[Anonymous No.11266753]

>>11266416
Frequency is how often is one photon fired or the wavelenght?

[Anonymous No.11266759]

>>11266752
>So 1watt laser and 2watt laser have different frequency?
How is that related to my OP?
>>11266753
Neither. It's the speed of light divided by wavelength.

[Anonymous No.11266760]

>>11266677
Cranky old man doesn't like a perfectly well defined word and writes a rambling paper about it

[Anonymous No.11266776]

>>11266759
some nanometers per second divided by meters indicates you measure photon in seconds.

Tick.

[Anonymous No.11266778]

>>11266760
It has some truth in it though, doesn't it? Phonon, photon, both are kinda bullshit terms because neither is an actual particle.

[Anonymous No.11266785]

>>11266776
The problem is, that stronger light still not produces more oscillation per second, therefore there is amplitude, or all lasers are not photon quanta.

Its simple as that.

[Anonymous No.11266786]

>>11266760
Anonymous 4channeller dismisses incredibly influential quantum physicist because he disagrees with the undergrad model of light

[Anonymous No.11266797]

Let's just suppose, beam of light of one wavelenght is still shitload of particles.

[Anonymous No.11266851]

>>11266778
>>11266786
A photon is a quantized mode of the electromagnetic field. It is defined in a completely analogous way to the way an electron is defined as a quantized mode of an electron field. They are both particles. A particle in quantum field theory does not mean a little localized ball, it means a quantized mode of a field.

Lamb was in his 80s when he wrote that paper and he is just being picky about language not physics, don't let it confuse you

[Anonymous No.11266867]

>>11266851
Thank you for the explanation. What about phonons?

[Anonymous No.11266886]

>>11266867
A phonon is exactly the same sort of thing. You write a Lagrangian where the field tells you about displacements of an atomic lattice. You break it up into modes, and each mode looks like a harmonic oscillator. A single excitation of one of these modes is called phonon. Since it has to do with displacements of a lattice it is like quantized sound, hence the name

[Anonymous No.11266904]

>>11266416
I remember Jon Baez having a long discussion on exactly this on his site, think it was called "photons schmotons" or something

The classical plane waves correspond to a particular superposition of energy eigenstates, known as coherent states, in some limit. Using this, the energy is proportional to the "amplitude" which is given by a quantum number alpha. I need to refresh myself how the energy becomes frequency independent

[Anonymous No.11266915]

>>11266904
I remember reading that email exchange between Baez and his student a long time ago and thinking it seemed kinda gay (literally)

[Anonymous No.11268427]

>>11266658
>does not satisfy any meaningful definition of "particle"
Congratulation, you just found out that the photon is neither wave nor particle. Welcome to the century after 1908.

>>11266666
kek'd and ch-ch-cheeecked!

[Anonymous No.11268449]

>>11268427
>the century after 1908.
the century after the century after 1908

[Anonymous No.11268455]

>>11268427
>Congratulation, you just found out that the photon is neither wave nor particle. Welcome to the century after 1908.
Except that e.g. electrons, which also have wave-particle duality, do satisfy meaningful definitions of particle. My argument is not that photons don't exist because they don't behave as classical particles, you nonce. It's abundantly clear you're in over your head here. This isn't a discussion for first-years.

[Anonymous No.11268462]

What the fuck is even going on in here?
There is not a single coherent thought in this thread. Learn to write English, you fuckwits.

[Anonymous No.11268466]

>>11266416
wavelength and frequency are inverses because photons travel at a fixed rate (i'm not sure if that is really true, it might just be popular mythology), the energy carried by any one photon is proportional to the frequency only, there are no other factors involved

[Anonymous No.11268469]

>>11268462
durr, I don't understand what's going on, must be everyone else's fault

>>11266658
A quick google search turns up this:
https://aapt.scitation.org/doi/full/10.1119/1.4955173

It's clearly sensible to talk about single photons, even if light from a laser is a superposition of photon number. I don't even get what you are arguing against

[Anonymous No.11268483]

As one anon already pointed out, the answer lies in the definition of a coherent state
https://en.wikipedia.org/wiki/Coherent_states

Basically, you construct a superposition of many photons of many different frequencies, and do so in such a way that removing any particular photon does not change the dynamics of the superposition (in the sense that they evolve to the same final state at a later time - this is the definition of a coherent state). The coherent state has a different frequency than any particular photon it is "composed" of, and this frequency is the one that is relevant to the macroscopic electric and magnetic fields.

In effect, this means that an electromagnetic wave of a particular energy and frequency is not necessarily composed of a definite number of photons with exactly the same frequency and identical energies. This is the case because in a coherent state, the total number of photons is uncertain.

[Anonymous No.11268499]

>>11268483
>The coherent state has a different frequency than any particular photon it is "composed" of, and this frequency is the one that is relevant to the macroscopic electric and magnetic fields
I'm pretty sure this is false

[Anonymous No.11268509]

>>11268499
that's how it works with harmonic oscillators. It's not an energy eigenstate, so it doesn't have the same frequency of any of the modes it's composed of. The coherent state is defined as an eigenstate of the annihilation operator, with some complex eigenvalue. The "phase" and "amplitude" of the coherent state are just that of this complex number. For the Gaussian wave packet in the simple harmonic oscillator case, this just determines the frequency that the wave packet goes back and forth, does it not?

I certainly don't mean frequency in the sense of it being an eigenvalue of the Hamiltonian. Pretty sure it's an abuse of language, if nothing else.

[Anonymous No.11268512]

>>11268509
>>11268483
to add, I haven't really read about this in quite some time but I remember seeing a good explanation in pic related (I'm sure there are other better sources, but this happens to be the one on my bookshelf)

[Anonymous No.11268523]

>>11268509
Coherent state is about about a superposition of particle number, not frequency. It is the amplitude and phase of the EM wave that are uncertain, not the frequency.

The harmonic oscillator has a specific unique frequency, and the coherent state rotates around phase space with that frequency. There is no superposition of frequency there.

[Anonymous No.11268535]

>>11268523
ok I'll defer to you.
happy new year

[Anonymous No.11268567]

>>11268455
>electrons satisfy meaningful definitions of particle
No, they don't. They are exactly like photons in that regard (disregarding other properties like charge, spin,...). See for example the double slit experiment.

>my argument is not that photons...
Who the fuck cares? I never said you did argue like that.

>you're over your head
Fucking retard. Projecting things I did not do to feel superior. Undergrads need to learn to read and understand before being allowed on the internet imho. You're pathetic.

[Anonymous No.11268569]

>>11268462
This. /sci/ is being invaded by retards.

[Anonymous No.11269351]

>>11268462
>>11268569
/sci/ indeed is full of retards but the retards are you.

[Anonymous No.11269440]

>>11269351
There's still worse people here. You can't deny that.